In traditional optical systems having reflecting and refracting surfaces, it is common to assume that the light passing through the system is limited to paraxial rays, specifically, rays that are near the optical axis and are sustained within small angles. However, practical optical systems rarely are limited to paraxial rays, and thus, the actual images assumed by gaussian optics often depart from the “perfect” image. This departure from the “perfect” image results in the introduction of distortion into the optical system, called aberrations. These aberrations are most problematic in small focal ratio optical systems where the angle from the optical axis is larger.
In a monochromatic optical system with only spherical surfaces, there are five (5) basic ray and wave aberrations, namely, spherical aberrations, coma, astigmatism, curvature of field, and distortion. Optical systems for use with multi-chromatic light have an additional source of distortion, namely, chromatic aberration.
Because the distortion introduced by aberrations into an optical system significantly degrades the quality of the images on the image plane of such system, there are significant advantages to the reduction of those aberrations. Various techniques are often used to minimize the aberrations. For example, in order to minimize spherical aberrations or coma, a lens may be “bent” to have different radii of curvature on opposite sides while maintaining a constant focal length, such as is contemplated by using the Coddington shape factor. Also, a pair of lenses, where one glass lens has a positive focal length, and the other made from a different glass has a negative focal length, are used together to correct spherical aberrator. One example of this technique is the “doublet” lens in which the two lenses have the same radius of curvature on the facing sides, and are cemented together.
Despite the available techniques to minimize the various aberrations, it is often difficult to simultaneously minimize all aberrations. In fact, corrections to an optical system to minimize one type of aberration may result in the increase in one of the other aberrations. Typically, one may decrease coma, at the expense of increasing spherical aberrations. Moreover, because it is often necessary to measure the aberrations only after an optical system is constructed due to additional aberrations from manufacturing or assembly tolerances, the creation of an optical system with minimal aberration typically requires several reconstructions before a suitable system is developed.
In complex optical systems, in addition to traditional aberration correction, it is often advantageous to create an optical element which generates a unique wavefront phase profile. Typically, these unique optical elements have been created by sophisticated grinding and polishing of traditional lenses. However, this method of manufacturing a unique optical element requires a significant amount of time and expertise, and results in a high cost of manufacturing the optical element.
Consequently, a need exists for the creation of an optical element which can generate a unique wavefront phase profile, and that can simultaneously minimize the chosen aberrations within an optical system.